The intelligence agency in the former Soviet republic of Kyrgyzstan has said that the man behind the deadly bombing on the St Petersburg subway is a Kyrgyz-born Russian citizen.

Eleven people were killed and more than 40 others injured when an explosion tore through a subway train under Russia's second-largest city on Monday.

There was no immediate claim of responsibility for the attack, which came while President Vladimir Putin was visiting the city, his hometown.

Kyrgyzstan's State Committee for National Security said in a statement on Tuesday that the man behind the bombing is a Kyrgyz-born Russian national. The intelligence agency said it is co-operating with Russian authorities to help the investigation.

It was unclear whether the attack was a suicide bombing or whether the bomber got away.

US President Donald Trump called Mr Putin to offer condolences over the attack.

The Kremlin said Mr Trump offered sympathy to the families of the blast victims of blast and asked President Putin to convey his support for the Russian people.

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Mr Putin thanked Mr Trump for the expression of solidarity, the Kremlin said, adding that the two leaders voiced a shared view that "terrorism is an evil that must be fought jointly".

The United Nations Security Council condemned "in the strongest terms the barbaric and cowardly terrorist attack".

Council members "expressed their deep sympathy and condolences to the victims of this heinous act of terrorism and to their families, and to the people and to the government of the Russian Federation", a statement said.

It added that the "perpetrators, organisers, financiers and sponsors of these reprehensible acts" should be brought to justice.

A woman lights a candle at an entrance to Sennaya subway station after an explosion in St.Petersburg subway in St.Petersburg, Russia (Image: AP Photo/Yevgeny Kurskov)

Mr Trump said it was "absolutely a terrible thing", White House press secretary Sean Spicer said. He said the US was prepared to offer assistance to Russia.

In the past two decades, Russian trains and planes have been frequent targets of attack, usually blamed on Islamic militants.

The Interfax news agency said on Monday that authorities believe the suspect, a 23-year old who came from ex-Soviet Central Asia and was linked to radical Islamic groups, carried the explosive device on to the train in a rucksack.

Within two hours of the blast, authorities had found and deactivated another bomb at another busy station, the anti-terror agency said. That station is a major transfer point for passengers on two lines and serves the railway station to Moscow.

The entire St Petersburg subway system was shut down and evacuated, but partial service resumed after about six hours.